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Consider a batch-sizing problem, where all jobs are identical or similar, and a unit processing time (p = 1) is specified for each job. To minimize the total completion time of jobs, partitioning jobs into batches may be necessary. Learning effect from setup repetition makes small-sized batches; on the contrary, job's learning effect results in large-sized batches. With their collaborative influence, we develop a forward dynamic programming (DP) algorithm to determine the optimal number of batches and their optimal integer sizes. The computation effort required by this DP algorithm is a polynomial function of job size.

We consider two-agent scheduling on a single machine, where there are job families and setup requirements exist between these families. Each agent's objective function is to minimize his own makespan. One of our goals is to find the optimal solution for one agent with a constraint on the other agent's makespan (constrained optimization). This problem is equivalent to the caudate Knapsack problem that we define in the paper. The other goal is to find single nondominated schedules (i.e., such that a better schedule for one of the two agents necessarily result in a worse schedule of the other agent), and to enumerate all nondominated schedules. Finally, two special cases, one with equal job processing times and the other with equal family setups are studied. We prove that the constrained optimization problems in both cases can be solved in polynomial time and that the cases have a polynomial number of nondominated schedules.

Open coast storm surge water levels consist of a wind shear forcing component generally referred to as a wind setup; a wave setup component caused by wind induced waves transferring momentum to the water column; an atmospheric pressure head component due to the atmospheric pressure deficit over the spatial extent of the storm system; a Coriolis forced component due to the effects of the rotation of the earth acting on the wind driven alongshore current at the coast; and, if astronomical tides are present, an astronomical tide component (although the tide is not really a direct part of the meteorological driven component of storm surge). Typically, the most important component of a storm surge is the wind setup component, especially on the East Coast of the US and in the Gulf of Mexico. The importance of bathymetry to this wind setup storm surge component is considered herein with special reference to the coastline of Florida where eight Florida transects consisting of a cross-section of bathymetric data perpendicular to the shoreline were investigated. Effects of Coriolis, wave setup, atmospheric pressure head, and astronomical tide are not considered herein but will be addressed in future papers. The present study findings show that the wind setup component can vary over an order of magnitude for the same wind speed depending on the bathymetry leading up to the coast.